Maharashtra State BoardHSC Science (General) 11th
Advertisement Remove all ads

Find the polar co-ordinates of points whose Cartesian co-ordinates are: (–1, –1) - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Sum

Find the polar co-ordinates of points whose Cartesian co-ordinates are:

(–1, –1)

Advertisement Remove all ads

Solution

Here, x = – 1 and y = – 1

∴ the point lies in the third quadrant.

Let the polar coordinates be (r, θ)

∴ r2 = x2 + y2 = ( – 1)2 + ( – 1)2 = 1 + 1 = 2

∴ r = `sqrt(2)`    ...[∵ r > 0]

tanθ = `y/x = (-1)/(-1)` = 1

Since the point lies in the third quadrant and 0 ≤ θ < 2π,

tanθ = 1

= tan 45°

= tan (180° + 45°) ...[∵ tanθ is periodic function with period π = 180°]

∴ tanθ = tan225°

∴ θ = 225°

∴ the polar coordinates of the given point are `(sqrt(2), 225^circ)`.

Concept: Polar Co-ordinate System
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×